Question 46
Find all infinite sequences $a_1, a_2, a_3, \dots$ of positive integers such that
a) $a_{nm} = a_n a_m$, for all positive integers $n, m$, and
b) there are infinitely many positive integers $n$ such that $\{1, 2, \dots, n\} = \{a_1, a_2, \dots, a_n\}$.
a) $a_{nm} = a_n a_m$, for all positive integers $n, m$, and
b) there are infinitely many positive integers $n$ such that $\{1, 2, \dots, n\} = \{a_1, a_2, \dots, a_n\}$.